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Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
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Cited by 45 (9 self)
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This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees are maintained via the linkcut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of kedge monotone chains in O(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and contract to be implemented in O(log n) time, leading to an improved method for spatial pointlocation in a 3dimensional convex subdivision. In addition, the interlacedtree approach is applied to online pointlo...
Methods for Achieving Fast Query Times in Point Location Data Structures
, 1997
"... Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data struc ..."
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Cited by 22 (1 self)
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Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data structures can be constructed so as to achieve O(log n) query times. But applications, such as those common in geographic information systems, motivate a reexamination of this problem with the goal of improving query times further while also simplifying the methods needed to achieve such query times. In this paper we perform such a reexamination, focusing on the issues that arise in three different classes of pointlocation query sequences: ffl sequences that are reasonably uniform spatially and temporally (in which case the constant factors in the query times become critical), ffl sequences that are nonuniform spatially or temporally (in which case one desires data structures that adapt to s...
Dynamization of the Trapezoid Method for Planar Point Location
, 1991
"... We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point ..."
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Cited by 15 (4 self)
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We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O(log n) time, while updates take O(log2 n) time. The space requirement is O(n log n). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time.
Monte Carlo Approximation of Form Factors with Error Bounded a Priori
, 1997
"... A R n ffl ffi ffi ffl O ffl ffi n n K n K A n M. Pellegrini April 16, 1996 11th ACM Symposium on Computational Geometry form factors occluded nonzero regular intersections Monte Carlo Approximation of Form Factors with Error Bounded a Priori A preliminary version of this paper appeared in Procee ..."
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Cited by 13 (1 self)
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A R n ffl ffi ffi ffl O ffl ffi n n K n K A n M. Pellegrini April 16, 1996 11th ACM Symposium on Computational Geometry form factors occluded nonzero regular intersections Monte Carlo Approximation of Form Factors with Error Bounded a Priori A preliminary version of this paper appeared in Proceedings of the , pages 287296, June 1995, Vancouver. Istituto di Matematica Computazionale del C.N.R. Via S. Maria 46, 56126 Pisa, Italy. tel: (+39) 50 593452 fax: (+39) 50 554342 email: pellegrini@imc.pi.cnr.it The exchange of radiant energy (e.g. visible light, infrared radiation) in simple macroscopic physical models is sometimes approximated by the solution of a system of linear equations (energy transport equations). A variable in such a system represents the total energy emitted by a discrete surface element. The coefficients of these equations depend on the between pairs of surface elements. A form factor is the fraction of energy leaving a surface element which directly reaches an...
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
"... Optimal dynamic vertical ray shooting in rectilinear planar subdivisions. In this paper we consider the dynamic vertical ray shooting problem, that is the task of maintaining a dynamic set S of n non intersecting horizontal line segments in the plane subject to a query that reports the first segment ..."
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Cited by 9 (0 self)
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Optimal dynamic vertical ray shooting in rectilinear planar subdivisions. In this paper we consider the dynamic vertical ray shooting problem, that is the task of maintaining a dynamic set S of n non intersecting horizontal line segments in the plane subject to a query that reports the first segment in S intersecting a vertical ray from a query point. We develop a linearsize structure that supports queries, insertions and deletions in O(log n) worstcase time. Our structure works in the comparison model and uses a RAM.
Improved Dynamic Planar Point Location (Extended Abstract)
"... We develop the first linearspace data structures for dynamic planar point location in general subdivisions that achieve logarithmic query time and polylogarithmic update time. 1 ..."
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We develop the first linearspace data structures for dynamic planar point location in general subdivisions that achieve logarithmic query time and polylogarithmic update time. 1